All publications herein are incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference. The following description includes information that may be useful in understanding the present subject matter. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed subject matter, or that any publication specifically or implicitly referenced is prior art.
Microscopy is a central tool in both the structural and functional study of biological systems. While light microscopy is of great utility, it is subject to several well-known limitations. Foremost among these is the resolution limit. The resolution limit of a light microscope is traditionally defined by the Rayleigh criterion, which is approximately
  R  =                    1.22        ⁢                                  ⁢        λ                    2        ⁢                                  ⁢        n        ⁢                                  ⁢        sin        ⁢                                  ⁢        α              =                  0.61        ⁢                                  ⁢        λ                    N        ⁢                                  ⁢        A            where λ is the wavelength, n is the index of refraction, and α is the half-angle of the maximum cone of light that can enter the entrance aperture of the objective lens. The term n sin α is often referred to as the numerical aperture (“NA”). As an example, in the context of light microscopy, a 40× oil immersion objective with a NA of 1.47 operating at a wavelength of 450 nm may resolve two points if they are at least 190 nm apart.
The Rayleigh criterion stems from the fact that electromagnetic waves are subject to diffraction and thus, there is a fundamental limit. Therefore, improving resolution requires either reducing the wavelength, which is not practical in biological applications, or increasing the numerical aperture. The latter is limited by the fact that α cannot exceed 90 degrees for physically realizable objectives.
One existing approach to increase the numerical aperture of a light microscope is to use two objectives to observe the subject specimen from opposing sides simultaneously. If both images are combined optically, the effective numerical aperture is doubled. This method has been reduced to practice and is identified as 4π microscopy (also know as 4PI or Scan4pi). 4π microscopy is derived from the fact that α can approach 90 degrees for an advanced microscope objective and that two of these objectives almost cover the full solid angle, which is 4πsrad. However, 4π microscopy requires the light from both objective lenses to be combined optically which requires precise alignment of the lenses. This need for precision leads to extreme alignment difficulties, which make 4π microscopy rather impractical and expensive.
An alternative to 4π microscopy is standing wave microscopy (see e.g., U.S. Pat. Nos. 5,671,085; 5,394,268; 5,801,881; 6,055,097; RE38,308; and 4,621,911). In standing wave microscopy a mirror is placed directly behind the subject specimen in an epi-fluorescence microscope. The subject specimen is illuminated through the microscope objective lens, and light passes through the subject specimen under investigation and is reflected back towards the objective lens by the mirror behind the subject specimen. Thus, the illumination light traverses the subject specimen twice, once from the objective lens towards the mirror and once from the mirror to the objective lens. In cases where the distance from the subject specimen to the mirror is less than half of the coherence length of the illumination light, an interference pattern that is periodic along the optical (z) axis will be observed:
      I    ⁡          (      z      )        =                                                E            forward                    ⁡                      (            z            )                          =                              E            backward                    ⁡                      (            z            )                                      =                  (                                            E              0                        ⁢                          sin              ⁡                              (                                                      ω                    ⁢                                                                                  ⁢                    t                                    +                                      zn                    λ                                                  )                                              +                                    E              0                        ⁢                          sin              ⁡                              (                                                      ω                    ⁢                                                                                  ⁢                    t                                    +                                                            n                      ⁡                                              (                                                                              2                            ⁢                                                                                                                  ⁢                                                          z                              m                                                                                -                          z                                                )                                                              λ                                                  )                                                    )            2      where z is the distance from the objective lens, E0 is the electrical field strength (also referred to as disturbance), λ is the wavelength of the light in a vacuum, n is the index of refraction,
  ω  =            2      ⁢                          ⁢      π      ⁢                          ⁢      f        =                  2        ⁢                                  ⁢        π        ⁢                                  ⁢        c            λ      is the angular frequency of the light in
      rad    s    ,t is the time and zm is the distance from the objective lens to the mirror. Integrating over one wave cycle leads to the observed average intensity:
      I    ⁡          (      z      )        =            E      0      2        ⁢    8    ⁢                  ⁢          π      (                        1          +                      cos            ⁡                          (                                                n                  λ                                ⁢                                  (                                                            2                      ⁢                                                                                          ⁢                                              z                        m                                                              -                                          2                      ⁢                      z                                                        )                                            )                                      ≈                  1          +                      cos            (                          φ              -                                                                    2                    ⁢                                                                                  ⁢                    n                                    λ                                ⁢                z                                      )                              
The significant property of this interference pattern is that its period is half that of the wavelength of the excitation light. In standing wave microscopy, this property is used to increase the axial resolution of the microscope. For this purpose, several images are obtained from the subject specimen by moving the mirror by a fraction of the wavelength, in the z-axis, relative to the stationary subject specimen and microscope objective. The images obtained in this fashion show only part of the subject specimen, namely the region which is illuminated by an interference maxima. Thus, it is possible to obtain a sequence of images, each corresponding to a different subject specimen depth. Because the interference pattern is periodic, the images obtained will contain features from multiple slices in instances where the subject specimen depth exceeds one-half of the wavelength and the extent of the objective's point spread function in the z-axis is greater than the interference pattern period. However, even in this case, standing wave microscopy is useful because it imposes a sharp axial structure on the point spread function which in turn aids deconvolution algorithms.
Standing wave microscopy can be combined with other microscopy methods, such as two-photon excitation and confocal microscopy to further improve the resolution along the z-axis and to resolve ambiguities that stem from the periodic nature of the interference pattern. Using standing wave microscopy, axial resolutions down to approximately 5 nm have been demonstrated. Standing wave effects have also been observed in photo-lithography, where the partial reflection from the substrate causes a periodic interference pattern perpendicular to the substrate surface, which in turn causes uneven exposure of the photo-resist. In this context, standing waves are an unwanted effect that degrades the performance of the photo-resist mask.
However, the primary constraint of standing wave microscopy stems from the fact that the interference pattern is produced by two counter-propagating planar or nearly planar wave-fronts. Thus, the interference pattern is periodic only along the z-axis axis and has no significant reading in the x-axis or y-axis. Therefore, only the resolution along the z-axis is improved, while the resolution along the x-axis and y-axis remains unchanged.
Accordingly, there is a need in the art for a method capable of improving resolution in wave microscopy. Furthermore, there exists a need in the art for a method capable of producing finite three-dimensional images of biological specimens in wave microscopy. To address these techniques, there is also a need in the art to develop a device that can improve resolution in wave microscopy and produce finite three-dimensional images in wave microscopy, all while reducing the complexities and costs associated with existing wave microscopy devices.